{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3LYEYS2BYJUQ2U44XBF64ZI4C2","short_pith_number":"pith:3LYEYS2B","canonical_record":{"source":{"id":"1509.00229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-01T11:17:52Z","cross_cats_sorted":["math.DS","math.OC"],"title_canon_sha256":"1c4fb26f6c6e25a1a4328bd7e3a1768bdf6a87afafe4b063250e9c0a867f9280","abstract_canon_sha256":"727b86e18607f6c733d22825336610dc01a19adca9ca1f0c473b7f534f1d3731"},"schema_version":"1.0"},"canonical_sha256":"daf04c4b41c2690d539cb84bee651c169e1f1f49bb1ff405b07ca26b0f638463","source":{"kind":"arxiv","id":"1509.00229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00229","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00229v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00229","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"3LYEYS2BYJUQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3LYEYS2BYJUQ2U44","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3LYEYS2B","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3LYEYS2BYJUQ2U44XBF64ZI4C2","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-01T11:17:52Z","cross_cats_sorted":["math.DS","math.OC"],"title_canon_sha256":"1c4fb26f6c6e25a1a4328bd7e3a1768bdf6a87afafe4b063250e9c0a867f9280","abstract_canon_sha256":"727b86e18607f6c733d22825336610dc01a19adca9ca1f0c473b7f534f1d3731"},"schema_version":"1.0"},"canonical_sha256":"daf04c4b41c2690d539cb84bee651c169e1f1f49bb1ff405b07ca26b0f638463","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:14.820764Z","signature_b64":"KoaWmwubsMMvHh5O2CBCAOh/lkA0yhs4tuMGe2x7j4lXQ2pITf/KoGpKXX4axP+hNeHmQOZMU/vzUHi/h8bUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf04c4b41c2690d539cb84bee651c169e1f1f49bb1ff405b07ca26b0f638463","last_reissued_at":"2026-05-18T01:34:14.819973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:14.819973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00229","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7P/tXz9lg+G9MxrwO7NApeGFsg/pjr6hVOgN3l5htxYVd04R/mEugoNnSDq5Op8AD48X5XKrjyDokykma/1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:27:23.477187Z"},"content_sha256":"9c627b1838bfe0b9b906331ebd0634b2a4e75b7da8d9b6a2f1bf57088b184afc","schema_version":"1.0","event_id":"sha256:9c627b1838bfe0b9b906331ebd0634b2a4e75b7da8d9b6a2f1bf57088b184afc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3LYEYS2BYJUQ2U44XBF64ZI4C2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A projection algorithm on measures sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.NA","authors_text":"IMT), Jonas Kahn, Nicolas Chauffert (PARIETAL), PARIETAL), Philippe Ciuciu (NEUROSPIN, Pierre Weiss (ITAV","submitted_at":"2015-09-01T11:17:52Z","abstract_excerpt":"We consider the problem of projecting a probability measure $\\pi$ on a set $\\mathcal{M}\\_N$ of Radon measures. The projection is defined as a solution of the following variational problem:\\begin{equation*}\\inf\\_{\\mu\\in \\mathcal{M}\\_N} \\|h\\star (\\mu - \\pi)\\|\\_2^2,\\end{equation*}where $h\\in L^2(\\Omega)$ is a kernel, $\\Omega\\subset \\R^d$ and $\\star$ denotes the convolution operator.To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with $N$ dots) or continuous line drawing (represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00229","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Le+NtrMrf2mr4EgV9evC+JXuEohyJASeH2KoIDh/EVNPRlASwKFKn2yNHEa1iQEsZzFRY6dLlXe3V0HG1BM1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:27:23.477852Z"},"content_sha256":"b3d0ed44b6316e0cae3a4baff874d0a152fbbea4e03ac95c2c077fc89861a7c0","schema_version":"1.0","event_id":"sha256:b3d0ed44b6316e0cae3a4baff874d0a152fbbea4e03ac95c2c077fc89861a7c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/bundle.json","state_url":"https://pith.science/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T05:27:23Z","links":{"resolver":"https://pith.science/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2","bundle":"https://pith.science/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/bundle.json","state":"https://pith.science/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LYEYS2BYJUQ2U44XBF64ZI4C2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3LYEYS2BYJUQ2U44XBF64ZI4C2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"727b86e18607f6c733d22825336610dc01a19adca9ca1f0c473b7f534f1d3731","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-01T11:17:52Z","title_canon_sha256":"1c4fb26f6c6e25a1a4328bd7e3a1768bdf6a87afafe4b063250e9c0a867f9280"},"schema_version":"1.0","source":{"id":"1509.00229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00229","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00229v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00229","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"3LYEYS2BYJUQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3LYEYS2BYJUQ2U44","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3LYEYS2B","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:b3d0ed44b6316e0cae3a4baff874d0a152fbbea4e03ac95c2c077fc89861a7c0","target":"graph","created_at":"2026-05-18T01:34:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the problem of projecting a probability measure $\\pi$ on a set $\\mathcal{M}\\_N$ of Radon measures. The projection is defined as a solution of the following variational problem:\\begin{equation*}\\inf\\_{\\mu\\in \\mathcal{M}\\_N} \\|h\\star (\\mu - \\pi)\\|\\_2^2,\\end{equation*}where $h\\in L^2(\\Omega)$ is a kernel, $\\Omega\\subset \\R^d$ and $\\star$ denotes the convolution operator.To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with $N$ dots) or continuous line drawing (represe","authors_text":"IMT), Jonas Kahn, Nicolas Chauffert (PARIETAL), PARIETAL), Philippe Ciuciu (NEUROSPIN, Pierre Weiss (ITAV","cross_cats":["math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-01T11:17:52Z","title":"A projection algorithm on measures sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00229","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9c627b1838bfe0b9b906331ebd0634b2a4e75b7da8d9b6a2f1bf57088b184afc","target":"record","created_at":"2026-05-18T01:34:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"727b86e18607f6c733d22825336610dc01a19adca9ca1f0c473b7f534f1d3731","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-09-01T11:17:52Z","title_canon_sha256":"1c4fb26f6c6e25a1a4328bd7e3a1768bdf6a87afafe4b063250e9c0a867f9280"},"schema_version":"1.0","source":{"id":"1509.00229","kind":"arxiv","version":1}},"canonical_sha256":"daf04c4b41c2690d539cb84bee651c169e1f1f49bb1ff405b07ca26b0f638463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daf04c4b41c2690d539cb84bee651c169e1f1f49bb1ff405b07ca26b0f638463","first_computed_at":"2026-05-18T01:34:14.819973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:14.819973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KoaWmwubsMMvHh5O2CBCAOh/lkA0yhs4tuMGe2x7j4lXQ2pITf/KoGpKXX4axP+hNeHmQOZMU/vzUHi/h8bUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:14.820764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c627b1838bfe0b9b906331ebd0634b2a4e75b7da8d9b6a2f1bf57088b184afc","sha256:b3d0ed44b6316e0cae3a4baff874d0a152fbbea4e03ac95c2c077fc89861a7c0"],"state_sha256":"42a3cf321385c71f9a11504cf7c8b4c3474a79820563abe1feadc67d4401b390"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWTq4J4lRYM1AgodtosyH9PPw3pju5oZCWkWptze+SpVy8gEJtjDtD+WixTSMLFcNDkWDhwL4cgOcK3g2x2/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:27:23.482266Z","bundle_sha256":"27a912d35bf2ad2c0379ffbc50c7192bea48a6eb0615ba6be153608304cbf5cc"}}